Internal problem ID [1974]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve((x-x*sqrt(x^2-y(x)^2))*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right )-\arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.529 (sec). Leaf size: 29
DSolve[(x-x*Sqrt[x^2-y[x]^2])*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]